Number of Subset of a Given Set

Q.

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A\times B$. Then

1. $y=273x$

2. $2y=91x$

3. $y=91x$

4. $2y=273x$

Q.

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is

1. 2⁹

2. None of these

3. 6

4. 8

Q. Let $S=\{0,1,5,4,7\}$. Then the total number of subsets of S is

1. 64
2. 40
3. 32
4. 20

Q. A set S has 7 elements. How many subsets having at most 5 elements does it have?

1. 125
2. 128
3. 116
4. 120

Q. Using binomial theorem, indicate which number is larger: $(1.1{)}^{10000}$ or $1000$

Q.

Write down all the subsets of the following sets.

(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) $\varphi$.

Q.

If n(A) = m and n(B)= n, find the total number of non-empty relations that can be defined from A to B.

Q.

Show that $\varphi ,\left\{0\right\}$ and 0 are all different.

Q.

Let $A=\left\{1,3,5,7,.......\right\}$$,$$B=\left\{x:x=2n-1,n\in N\right\}$ and $C=\left\{x:x=4n-1,n\in N\right\}.$ Prove that $C\ne B$

Q. If $R\subset A\times B$ and $S\subset B\times C$ be two relations, then $(SoR{)}^{-1}$ =

1. S^-1 oR^-1

2. R^-1oS^-1

3. SoR

4. RoS

Q.

$If\left(x\right)=x^{n}andif{f}^1\left(1\right)=10thenn=$

1. 10

2. 2

3. 100

4. 1

Q. Two finite sets have $m$ and $n$ number of elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. Then $m$ and $n$ are

1. $7,6$
2. $6,3$
3. $5,1$
4. $8,7$

Q.

Let $A=\left\{1,3,5,7,.......\right\}$$,$$B=\left\{x:x=2n-1,n\in N\right\}$ and $C=\left\{x:x=4n-1,n\in N\right\}.$ Prove that $A=B$

Q.

If $A=\{1,2\}andB=\{3,4\}$ how many subsets will $A\times B$

Q. A set contains 2n+1 elements. The number of subsets of this set containing more than n elements is equal to

1. $2^{n-1}$
2. $2^{n+1}$
3. $2^n$
4. $2^{2n}$

Q. Make correct statements by filling in the symbols $\subset$ or $\subset ̸$ in blank spaces:
(i) $\{2,3,4\}......\{1,2,3,4,5\}$
(ii) $\{a,b,c\}...\{b,c,d\}$
(iii) {$x:x$ is a student of Class XI of your school}. . .{$x:x$ student of your school}
(iv) {$x:x$ is a circle in the plane} . . .{$x:x$ is a circle in the same plane with radius 1 unit}
(v) {$x:x$ is a triangle in a plane} . . . {$x:x$ is a rectangle in the plane}
(vi) {$x:x$ is an equilateral triangle in a plane} . . . {$x:x$ is a triangle in the same plane}
(vii) {$x:x$ is an even natural number} . . . {$x:x$ is an integer}

Q.

Let set A = {a, b, c, d} and set B = {4, 8, 16, 32). If the total number of relations from A to B is $2^x$ find the value of $\frac{\left(x\right)}{2}$?

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Q. The number of subsets of the power set of a singleton set is

1. $1$
2. $2$
3. $4$
4. $16$

Q. The number of non-empty subsets of the set $\{1,2,3,4\}$ is

1. 14
2. 15
3. 16
4. 17

Q.

A set S has 7 elements. How many subsets having at most 5 elements does it have?

1. 128

2. 125

3. 120

4. 116

Q. Find the number of subsets of a set whose set contains $6$ elements.